The overall goal of the proposed research is to explore the mechanistic features and synthetic potential of chiral dioxiranes. The specific aims of the proposed research are: (1) to understand the mechanism and transition states involved in asymmetric epoxidation of olefins by chiral dioxiranes; (2) to further design and search for new ketone catalysts with high stability, reactivity, and enantioselectivity; (3) to explore and expand the scope of dioxirane-mediated asymmetric epoxidation; (4) to apply the newly developed asymmetric epoxidation to the synthesis of useful chiral building blocks and biologically active compounds. [unreadable] [unreadable]